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Minimum aberration $$(S^2)S^{n-k}$$ designs. (English) Zbl 0967.62056
Summary: This paper extends the $$4^m2^n$$ minimum aberration designs (MA designs) of C.F.J. Wu and R. Zhang [Biometrika 80, No. 1, 203-209 (1993; Zbl 0769.62058)] to the case of $$(S^2)S^{n-k}$$, where $$S$$ is any prime or prime power. Some basic properties of $$(S^2)S^{n-k}$$ MA designs, including the relations with $$S^{n-k}$$ MA designs, are discussed. The $$(9)3^{n-k}$$ MA designs with 27 runs and $$(16)4^{n-k}$$ MA designs with 64 runs are tabulated, and some $$(4)2^{n-k}$$ MA designs are constructed using the above relations.

##### MSC:
 62K15 Factorial statistical designs